ATON is a hopefully evolving classification theory. It aspires to unify knowledge around numbers and prefers naive methods. Some of the older posts are wrong but I'll keep them for the sake of continuity.

Sunday, March 26, 2006

Mirror Set and the elementary particles

Now revised;
http://a-theory-of-nothingness.blogspot.com/2006/11/mirror-set-rev-1.html

Mirror Set of order n is the (n+1)*(n+1) matrix quotient set;
Mn=Mnkl=Ek/Hl, (k,l)=0,...,n

M6 seems interesting with the following main diagonal state quotients and proposed mappings to elementary particles;
SE0/SH0=1 ... Higgs?
SE1/SH1=1/2 ... Light
SE2/SH2=1/2 ... Weak
SE3/SH3=3/2 ... Quarks
SE4/SH4=18 ... Leptons
SE5/SH5=1080 ... Space-Time-like?
SE6/SH6=388800 ... Mass-Gravity-like?
The digits of 4,5,6 all add to multiples of 9.
388800/1080=360
1080/18=60
18/3/2=12
3/2/1/2=3
1/2/1/2=1
1/2/1=1/2

3/2 is the symmetry of quarks and equal tempered tuning.
Quarks come in 3 generations and 2 types;
{{u,d},{c,s},{t,b}}
I put 3/2 in the middle and proposed M6 since energy seems to be balanced around quarks. This balancing is achieved by the large mass ratio Mp/Me=1836.
When the state quotient is expressed more explicitely it becomes clearer;
E3/H3={,{},{,{}}}/{,{,{,{}}}}
SE3/SH3=3!2!1!0!/2^3=12/8=3*2*2/2*2*2=3/2
There is 2*2*3 ness (3 generations, 2*2 types) and 2*2*2 ness (3 color/anti-color pairs) at the same time.

18=2*3*3 is the number for leptons.
Leptons also come in 3 generations and 2 types;
{{e,ve},{m,vm},{t,vt}}
18 is pretty obvious in the periodic table, displaying the 18-slot lepton wrapping of the nucleus.
6 is is kinda explained but how about 3*6=18, why does it get multiplied by 3?
Maybe leptons are satisfying the color multiplicity of quarks.

1/2 is degenerate curiously.
The first 1/2 has to be light, electric and magnetic together make one unit.
The second 1/2 then stands for weak, with W+,Z0,W-.
The degeneracy may stand for the realtively easy light-weak unification.

1 must be Higgs which is assumed to be scalar and not detected yet.

I made a guess about what the other two are, 1080 and 388800, space-time-like and mass-gravity-like.
Gravity seems to be a deeper field as black hole theories suggest.
Space-Time stop at the event horizon but Mass-Gravity don't.
Putting quarks in the middle suggests the couplings;
{Higgs,Mass-Gravity}
{Light,Space-Time}
{Weak,Leptons}
Weak-Lepton coupling is observed in the decay of neutron;
n->p+e+ve
Light-Space-Time coupling is pretty obvious.
We define Space-Time with light.
Higgs-Mass-Gravity coupling remains to be seen.

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